I admit that I overuse ellipses. I frequently use them to imply an extended wait, during which time I am left speechless after hearing something mind blowing. However, elipses in this case take on a different tone.
When you say , "Bye..." it implies that there are unsaid thoughts. The easiest interpretation is, "Bye...your leaving because you don't like me, but I'm just too hurt by this terrible affront to say anything". It comes across as accusing them of being a negligent friend for needing to leave. Ive also seen people who use ellipses instead of commas, so just because it's easy to read that way, doesn't mean that is what you were implying. Elipses move into the AOLspeak vernacular has led to me, in turn, toward using it a lot less. I'd never heard the term, "Emo Dots", but it is unfortunately accurate.
Also, if you just explained ellipses in a short sentence, you would have been fine. Giving a Wikipedia link just sounds like you're trying to belittle her with a scholastic authority, not trying to inform her. Fine, you may be a smartass, but in that case you have no right to complain when someones insulted. Free speech includes responsibility.